I doubt it and even if it does I do not think the PSU that comes with that system would give enough power.
From what I can tell that card is still full height so there is no way it will fit in a case that is only 4 inches wide sorry. That card is not as long but still retains full height from what I can tell.
You would be better off saving your money and building a new rig rather than putting any money into that PC.